{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YKS2WPDIALORJF3EH756YITF2O","short_pith_number":"pith:YKS2WPDI","canonical_record":{"source":{"id":"1509.03991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-14T08:38:44Z","cross_cats_sorted":[],"title_canon_sha256":"0e4a1ce55a1517bd1b9379f318b77f3c206b232a6c9b544f14fe617684f3d72e","abstract_canon_sha256":"986f61db9033e0524d03f5d12f099437fb6615862c146568c978cddb530ea39f"},"schema_version":"1.0"},"canonical_sha256":"c2a5ab3c6802dd1497643ffbec2265d392f4b84a2c1003ac9de08af6f136eda6","source":{"kind":"arxiv","id":"1509.03991","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03991","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03991v2","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03991","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"pith_short_12","alias_value":"YKS2WPDIALOR","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YKS2WPDIALORJF3E","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YKS2WPDI","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YKS2WPDIALORJF3EH756YITF2O","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-14T08:38:44Z","cross_cats_sorted":[],"title_canon_sha256":"0e4a1ce55a1517bd1b9379f318b77f3c206b232a6c9b544f14fe617684f3d72e","abstract_canon_sha256":"986f61db9033e0524d03f5d12f099437fb6615862c146568c978cddb530ea39f"},"schema_version":"1.0"},"canonical_sha256":"c2a5ab3c6802dd1497643ffbec2265d392f4b84a2c1003ac9de08af6f136eda6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:53.731042Z","signature_b64":"6Lc+qCL1ropEGfFJDzTGCdb1+fEywfTH1xkkesZctwheUo1gnYy5PSecE6VvzDGO9N4I8xlBH2GsKaiYPEhkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2a5ab3c6802dd1497643ffbec2265d392f4b84a2c1003ac9de08af6f136eda6","last_reissued_at":"2026-05-18T01:00:53.730301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:53.730301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03991","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nN+m+nzZaR1BVYaQTxGLiAmaFtoChizH/xCxiLPaw41l+rAgD9qI1fe2gYfbIIU46gSR6sMhpEOjo2x80R4hCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:14:09.371397Z"},"content_sha256":"61a21def80ff8c0b62c30ee08c792d2ebbfc308b098170438252ab320463ec59","schema_version":"1.0","event_id":"sha256:61a21def80ff8c0b62c30ee08c792d2ebbfc308b098170438252ab320463ec59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YKS2WPDIALORJF3EH756YITF2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiscale methods for problems with complex geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Axel M{\\aa}lqvist, Daniel Elfverson, Mats G. Larson","submitted_at":"2015-09-14T08:38:44Z","abstract_excerpt":"We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We construct corrected coarse test and trail spaces which takes the fine scale features of the computational domain into account. The corrections only need to be computed in regions surrounding fine scale geometric features. We achieve linear convergence rate in energy norm for the multiscale solution. Moreover, the conditioning of the resulting matrices is not affe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03991","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FjScHVEnj9brZbQyw0lMgdQ6PumhhpoNYddM5oejvMZIl5o+7P9RT2xI1OoOC3GI/9NwM7jvLlCj3CE7/pzVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:14:09.372044Z"},"content_sha256":"2fdd437b1bf6d64c4e0d594e8fc1167a772a1c18b384515df3985a9cf8c9e84e","schema_version":"1.0","event_id":"sha256:2fdd437b1bf6d64c4e0d594e8fc1167a772a1c18b384515df3985a9cf8c9e84e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKS2WPDIALORJF3EH756YITF2O/bundle.json","state_url":"https://pith.science/pith/YKS2WPDIALORJF3EH756YITF2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKS2WPDIALORJF3EH756YITF2O/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T19:14:09Z","links":{"resolver":"https://pith.science/pith/YKS2WPDIALORJF3EH756YITF2O","bundle":"https://pith.science/pith/YKS2WPDIALORJF3EH756YITF2O/bundle.json","state":"https://pith.science/pith/YKS2WPDIALORJF3EH756YITF2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKS2WPDIALORJF3EH756YITF2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YKS2WPDIALORJF3EH756YITF2O","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"986f61db9033e0524d03f5d12f099437fb6615862c146568c978cddb530ea39f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-14T08:38:44Z","title_canon_sha256":"0e4a1ce55a1517bd1b9379f318b77f3c206b232a6c9b544f14fe617684f3d72e"},"schema_version":"1.0","source":{"id":"1509.03991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03991","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03991v2","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03991","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"pith_short_12","alias_value":"YKS2WPDIALOR","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YKS2WPDIALORJF3E","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YKS2WPDI","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:2fdd437b1bf6d64c4e0d594e8fc1167a772a1c18b384515df3985a9cf8c9e84e","target":"graph","created_at":"2026-05-18T01:00:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We construct corrected coarse test and trail spaces which takes the fine scale features of the computational domain into account. The corrections only need to be computed in regions surrounding fine scale geometric features. We achieve linear convergence rate in energy norm for the multiscale solution. Moreover, the conditioning of the resulting matrices is not affe","authors_text":"Axel M{\\aa}lqvist, Daniel Elfverson, Mats G. Larson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-14T08:38:44Z","title":"Multiscale methods for problems with complex geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03991","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:61a21def80ff8c0b62c30ee08c792d2ebbfc308b098170438252ab320463ec59","target":"record","created_at":"2026-05-18T01:00:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"986f61db9033e0524d03f5d12f099437fb6615862c146568c978cddb530ea39f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-14T08:38:44Z","title_canon_sha256":"0e4a1ce55a1517bd1b9379f318b77f3c206b232a6c9b544f14fe617684f3d72e"},"schema_version":"1.0","source":{"id":"1509.03991","kind":"arxiv","version":2}},"canonical_sha256":"c2a5ab3c6802dd1497643ffbec2265d392f4b84a2c1003ac9de08af6f136eda6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2a5ab3c6802dd1497643ffbec2265d392f4b84a2c1003ac9de08af6f136eda6","first_computed_at":"2026-05-18T01:00:53.730301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:53.730301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Lc+qCL1ropEGfFJDzTGCdb1+fEywfTH1xkkesZctwheUo1gnYy5PSecE6VvzDGO9N4I8xlBH2GsKaiYPEhkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:53.731042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61a21def80ff8c0b62c30ee08c792d2ebbfc308b098170438252ab320463ec59","sha256:2fdd437b1bf6d64c4e0d594e8fc1167a772a1c18b384515df3985a9cf8c9e84e"],"state_sha256":"7931d51c03efcfac5b976010a5ad376b0fd9084a81384acf43d1cdd8f6adb818"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y1MiZ1e/PXQkbY5qPMMY9HHIFHfE5fwPjL7iOzwQlUJsaTIBffF9db2LLT77tQE5kBs1wcuNnJpY59mVJBzxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:14:09.375273Z","bundle_sha256":"48a901cc3ad62e47e37b61d61eb6210bb40b9775ad278a214edab20e2ea7edae"}}